Is sech^2(x)+tanh^2(x)=1 ?

The answer to whether sech^2(x)+tanh^2(x)=1 is True

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prove sech^2(x)+tanh^2(x)=1

prove

sech^{2} (x) + tanh^{2} (x) = 1

True

Solution steps

sech^{2} (x) + tanh^{2} (x) = 1

Use the Hyperbolic identity:

sech^{2} (x) = 1 - tanh^{2} (x)

sech^{2} (x) + tanh^{2} (x) = 1

\Rightarrow True

sec (x) cos (x) - 2 cos^{2} (x) = - (cos (2 x))

2 cos^{2} (A) - cos (2 A) - 1 = 0

\frac{( 2 sec ( x ) )}{tan ( x )} = 2 csc (x)

\frac{cot ( x ) + 1}{cos ( x ) + sin ( x )} = csc (x)

sec^{2} (y) = (sec (y))^{2}